A Computer-Assisted Uniqueness Proof for a Semilinear Elliptic Boundary Value Problem

A wide variety of articles, starting with the famous paper (Gidas, Ni and Nirenberg in Commun. Math. Phys. 68, 209-243 (1979)) is devoted to the uniqueness question for the semilinear elliptic boundary value problem -{\Delta}u={\lambda}u+u^p in {\Omega}, u>0 in {\Omega}, u=0 on the boundary of {\Omega}, where {\lambda} ranges between 0 and the first Dirichlet Laplacian eigenvalue. So far, this question was settled in the case of {\Omega} being a ball and, for more general domains, in the case {\lambda}=0. In (McKenna et al. in J. Differ. Equ. 247, 2140-2162 (2009)), we proposed a computer-assisted approach to this uniqueness question, which indeed provided a proof in the case {\Omega}=(0,1)x(0,1), and p=2. Due to the high numerical complexity, we were not able in (McKenna et al. in J. Differ. Equ. 247, 2140-2162 (2009)) to treat higher values of p. Here, by a significant reduction of the complexity, we will prove uniqueness for the case p=3

Metamaterials proposed as perfect magnetoelectrics

Magnetoelectric susceptibility of a metamaterial built from split ring resonators have been investigated both experimentally and within an equivalent circuit model. The absolute values have been shown to exceed by two orders of magnitude that of classical magnetoelectric materials. The metamaterial investigated reaches the theoretically predicted value of the magnetoelectric susceptibility which is equal to the geometric average of the electric and magnetic susceptibilities.Comment: 5 pages, 3 figure

Nonlinear Elasticity of Single Collapsed Polyelectrolytes

Nonlinear elastic responses of short and stiff polyelectrolytes are investigated by dynamic simulations on a single molecule level. When a polyelectrolyte condensate undergoes a mechanical unfolding, two types of force-extension curves, i.e., a force plateau and a stick-release pattern, are observed depending on the strength of the electrostatic interaction. We provide a physical interpretation of such force-extension behavior in terms of intramolecular structures of the condensates. We also describe a charge distribution of condensed counterions onto a highly stretched polyelectrolyte, which clarifies a formation of one-dimensional strongly correlated liquid at large Coulomb coupling regime where a stick-release pattern is observed. These findings may provide significant insights into the relationship between a molecular elasticity and a molecular mechanism of like-charge attractions observed in a wide range of charged biopolymer systems.Comment: 5pages, 5figure

Twisted split-ring-resonator photonic metamaterial with huge optical activity

Coupled split-ring-resonator metamaterials have previously been shown to exhibit large coupling effects, which are a prerequisite for obtaining large effective optical activity. By a suitable lateral arrangement of these building blocks, we completely eliminate linear birefringence and obtain pure optical activity and connected circular optical dichroism. Experiments at around 100-THz frequency and corresponding modeling are in good agreement. Rotation angles of about 30 degrees for 205nm sample thickness are derived.Comment: 6 pages, 4 figure

Экспериментальные исследования периодического способа питания забоя скважин дробью

High power diode lasers have become an established source for numerous direct applications like metal hardening and polymer welding due to their high efficiency, small size, low cost and high reliability. These laser sources are also used for efficient pumping of solid state lasers as Nd:YAG lasers. To increase the output power of diode lasers up to several kilowatts, the emitters are scaled laterally by forming a diode laser bar and vertically by forming a diode laser stack. For most applications like hardening and illumination, though, the undefined far field distribution of most commercially available high power diode laser stacks states a major drawback of these devices. As single emitters and bars can fail during their lifetime, the near field distribution does not remain constant. To overcome these problems, the intensity distribution can be homogenized by a waveguide or by microoptic devices. The waveguide segments the far field distribution by several total internal reflections, and these segments are overlaid at the waveguide's exit surface. By the microoptic device, the near field is divided into beamlets which are overlaid by a field lens. Both approaches are presented, and realized systems are described

Sub-cortical and brainstem sites associated with chemo-stimulated increases in ventilation in humans

We investigated the neural basis for spontaneous chemo-stimulated increases in ventilation in awake, healthy humans. Blood oxygen level dependent (BOLD) functional MRI was performed in nine healthy subjects using T2weighted echo planar imaging. Brain volumes (52 transverse slices, cortex to high spinal cord) were acquired every 3.9 s. The 30 min paradigm consisted of six, 5-min cycles, each cycle comprising 45 s of hypoxic-isocapnia, 45 s of isooxic-hypercapnia and 45 s of hypoxic-hypercapnia, with 55 s of non-stimulatory hyperoxic-isocapnia (control) separating each stimulus period. Ventilation was significantly (p < 0.001) increased during hypoxic-isocapnia, isooxic-hypercapnia and hypoxic-hypercapnia (17.0, 13.8, 24.9 L/min respectively) vs. control (8.4 L/min) and was associated with significant (p < 0.05, corrected for multiple comparisons) signal increases within a bilateral network that included the basal ganglia, thalamus, red nucleus, cerebellum, parietal cortex, cingulate and superior mid pons. The neuroanatomical structures identified provide evidence for the spontaneous control of breathing to be mediated by higher brain centres, as well as respiratory nuclei in the brainstem

Visual Physics Analysis (VISPA) - Concepts and First Applications

VISPA is a novel development environment for high energy physics analyses, based on a combination of graphical and textual steering. The primary aim of VISPA is to support physicists in prototyping, performing, and verifying a data analysis of any complexity. We present example screenshots, and describe the underlying software concepts.Comment: Parallel talk at ICHEP08, Philadelphia, USA, July 2008. 4 pages, 2 figure

RGCL at GermEval 2019: offensive language detection with deep learning

This paper describes the system submitted by the RGCL team to GermEval 2019 Shared Task 2: Identification of Offensive Language. We experimented with five different neural network architectures in order to classify Tweets in terms of offensive language. By means of comparative evaluation, we select the best performing for each of the three subtasks. Overall, we demonstrate that using only minimal preprocessing we are able to obtain competitive results